# Online Cosine Calculator

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# Cosine Calculator

In order to calculate cos(x) on the calculator:

Enter the input angle. Select angle type of degrees (°) or radians (rad) in the combo box. Press the = button to calculate the result.

## Inverse cosine calculator

Enter the cosine value, select degrees (°) or radians (rad) and press the = button:

### Cosine Calculator

The cosine calculator is a twin tool of our sine calculator - add to them the tangent tool and you'll have a pack of the most popular trigonometric functions. Simply type the angle - in degrees or radians - and you'll find the cosine value instantly. The cosine calculator helps to find out the cosine value for a specific angle in degrees or radians.

** Cosine definition**

In a right triangle ABC the sine of α, sin(α) is defined as the ratio betwween the side adjacent to angle α and the side opposite to the right angle (hypotenuse):

cos α = b / c

Example

b = 3"

c = 5"

cos α = b / c = 3 / 5 = 0.6

** How to Use the Cosine Calculator?**

In order to calculate cos(x) on the calculator:

1. Enter the input angle.

2. Select angle type of degrees (°) or radians (rad) in the combo box.

3. Press the = button to calculate the result.

** What is cosine?**

Cosine is one of the most basic trigonometric functions. It may be defined on the basis of right triangle or unit circle, in analogical way as the sine is defined:

The cosine of an angle is the length of the adjacent side divided by the length of the hypotenuse.

cos(α) = adjacent / hypotenuse = b / c

Right triangle: illustration of the cosine definition. Adjacent side over a hypotenuse. The cosine function may be defined that way: as the sine of the complementary angle - the other non-right angle. The abbreviation of cosine is cos, e.g. cos(30°).

** Cosine function :-**The cosine is a trigonometric function of an angle, usually defined for acute angles within a right-angled triangle as the ratio of the length of the adjacent side to the hypotenuse. It is the complement to the sine. In the illustration below, cos(α) = b/c and cos(β) = a/c.

Since cos(α) = b/c, from this definition it follows that the cosine of any angle is always less than or equal to one, and it can take negative values. The cosine of a 90-degree angle is equal to zero, since in order to calculate it we would need a triangle with two 90-degree angles, which is the definition of a straight line. As the third side of the triangle does not exist (length is 0), the cosine equals zero (0 divided by the length of the hypotenuse equals 0). You can use this cosine calculator to verify this.

A commonly used law in trigonometry which is trivially derived from the cosine definition is the law of cosines: c^{2} = a^{2} + b^{2} - 2ab·cosγ

Important properties of a cosine function:

1. Range (codomain) of a cosine is -1 ≤ cos(α) ≤ 1

2. Cosine period is equal to 2π

3. It's an even function (while sine is odd!), which means that cos(-α) = cos(α)

4. Cosine definition is essential to understand the law of cosines - a very useful law to solve any triangle.